Drilling Engineering
Prepared by: Tan Nguyen
Drilling Engineering - PE 311
Laminar Flow in Pipes and Annuli
Non-Newtonian Fluids
Drilling Engineering
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When attempting to quantify the pressure losses in side the drillstring and in the annulus it is
worth considering the following matrix:
Frictional Pressure Drop in Pipes and Annuli
Drilling Engineering
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Pipe Flow – Power Law Fluids
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Pipe Flow – Power Law Fluids
Frictional pressure drop in field unit:
Drilling Engineering
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Annular Flow – Power Law Fluids
Frictional pressure drop in field unit:
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Pipe Flow – Bingham Fluids
Drilling Engineering
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Pipe Flow – Bingham Fluids
Drilling Engineering
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Pipe Flow – Bingham Fluids
Frictional pressure drop in field unit:
Drilling Engineering
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Annular Flow – Bingham Fluids
Frictional pressure drop in field unit:
Drilling Engineering
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Summary
Drilling Engineering
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Examples
Example 1: A Cement slurry that has a flow-behavior index of 0.3 and a consistency index of
9400 eq cp is being pumped in an 8.097x4.5 in. annulus at a rate of 200 gal/min. Assuming the
flow pattern is laminar, compute the frictional pressure loss per 1000 ft of annulus. Also
estimate the shear rate at the pipe wall.
Mean velocity:
Frictional pressure loss:
Shear rate at the pipe wall:
11
12
sec128)3.0/12(5.4097.8
803.1*48248
nw
w ddv
sftdd
qv /803.1)5.4097.8(488.2
80488.2 222
122
ftpsiftpsi
ddvK
dLdp n
nn
n
1000/9.77/0779.00.02080.312
4.5)097144,000(8.3)9,400(1.80
0208.02
144000
0.3
1.3
0.31
112
Drilling Engineering
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Examples
Example 2:
a. Calculate the velocity of a fluid flowing through a 5’’ 19.5 lbm/ft drillpipe with I.D. = 4.276’’ at
150 GPM.
b. Determine the pressure loss in the above situation if the fluid is a Bingham Plastic fluid with
a plastic viscosity of 20 cp, a yield point of 15 lbf/100ft2 and density of 10 ppg. (1 lbf/100ft2 =
0.479 Pa)
c. Calulate the pressure loss in the above situation if the fluid was a power law fluid with the
flow behavior index of 0.75 and a consistency index of 70 eq cp. (lbfxSn/100ft2 = 479 eq cp)
Drilling Engineering
Prepared by: Tan Nguyen
Examples
Solution:
a. Calculate the velocity of a fluid flowing through a 5’’ 19.5 lbm/ft drillpipe with I.D. = 4.276’’ at
150 GPM.
b. Determine the pressure loss in the above situation if the fluid is a Bingham Plastic fluid with
a plastic viscosity of 20 cp, a yield point of 15 lbf/100ft2 and density of 10 ppg.
c. Calulate the pressure loss in the above situation if the fluid was a power law fluid with the
flow behavior index of 0.75 and a consistency index of 70 eq cp.